Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 65

The scores for the alternative y 5 obtained by the WlFBM

Fig. 1.11 The scores for the alternative y 5 obtained by the WIFBM

and Yager (2011)'s method are smaller than 0, which could indicate that Xia et al.
(2012a)'s method is more optimistic, while the one given by Xu and Yager (2011)
is more pessimistic. Thus, we can choose the right one according to the practical
problem and the experts' risk preferences.

1.5 Generalized Intuitionistic Fuzzy Bonferroni Means

1.5.1 Generalized Bonferroni Means

Let p be a collection of nonnegative numbers.

Beliakov et al. (2010) further extended the Bonferroni means by considering the
correlations of any three aggregated arguments instead of any two:

, q , r ≥ 0, and a i ( i = 1 , 2 ,..., n )

Definition 1.10 (Beliakov et al. 2010) If

⎛ ⎞

1

p + q + r

n

⎝ ⎠

1

a p
i

a q

GBM p , q , r

j a k

( a 1 , a 2 ,..., a n ) =

n ( n − 1 )( n − 2 )

1
i = j = k

i , j , k =

(1.145)

then GBM p , q , r is called a generalized Bonferroni mean (GBM).